Abstract

The magnetic chemically peculiar (CP2) stars of the upper main sequence are well-suited for investigating the
impact of magnetic fields on the surface layers of stars, which leads to abundance inhomogeneities (spots)
resulting in photometric variability. The light changes are explained in terms of the oblique rotator model;
the derived photometric periods thus correlate with the rotational periods of the stars. CP2 stars exhibiting
this kind of variability are classified as α2 Canum Venaticorum (ACV) variables. We have analysed around
3 850 000 individual photometric WASP measurements of magnetic chemically peculiar (CP2) stars and candidates
selected from the Catalogue of Ap, HgMn, and Am stars, with the ultimate goal of detecting new ACV variables.
In total, we found 80 variables, from which 74 are reported here for the first time. The data allowed us to
establish variability for 23 stars which had been reported as probably constant in the literature before.
Light curve parameters were obtained for all stars by a least-squares fit with the fundamental sine wave and its first harmonic.
Because of the scarcity of Strömgren uvbyβ measurements and the lack of parallax measurements with an accuracy better
than 20%, we are not able to give reliable astrophysical parameters for the investigated objects.

1 Introduction

The group of chemically peculiar (CP) stars on the upper main sequence displays peculiar lines and line strengths,
in addition to other peculiar features such as a strong global stellar magnetic field (Babcock 1947).
One can usually distinguish between Am (CP1), Si as well as SrCrEu (CP2), HgMn (CP3), and He-weak/strong (CP4) stars
(Preston 1974). The subgroup of CP2 objects, which comprises B to F-type stars, is characterized by variable
line strengths and radial velocity changes as well as photometric variability of in general the same periodicity.
CP2 stars typically have overabundances of up to several dex for Si, Sr, Cr, Eu, and other rare earth elements as
compared to the Sun (Saffe et al. 2005);
the overabundances of the respective elements are strongly correlated with effective temperature.

Photometric variability of the CP2 star α2 Canum Venaticorum (ACV) was first reported by Guthnik & Prager (1914).
The light curves of CP stars can be fitted well by a sine wave and its first harmonic with varying amplitudes
depending on the photometric filter systems (North 1984). For some CP stars, a double-wave structure of the
photometric light curves depending on the observed wavelength region is detected (Maitzen 1980).
However, similar magnetic field modulus variations are rather rare exceptions (Mathys et al. 1997).

The variability of CP2 stars is explained in terms of the oblique rotator model (Stibbs 1950),
according to which the period of the observed variations
is simply the rotational period. Accurate knowledge of the rotational period and its evolution in
time is a fundamental step in understanding the complex behaviour of CP2 stars, especially as
far as it concerns the phase relation between the magnetic, spectral, and light variations (Mikulášek et al. 2010).

Recently, Balona et al. (2015) presented an analysis of the light curves of 29 CP1 stars from the Kepler
satellite mission. They found 12 δ Scuti variables, one γ Doradus star and 10 stars,
whose variability is in accordance with rotational modulation caused by spots.
However, the amplitudes of the detected variability is between 4 and 200 ppm which, normally, cannot be
achieved via ground based observations.
This demonstrates that, apparently, even this subgroup of CP stars shows rotationally induced variability.
However, Aurière et al. (2010) found that none of the 15 investigated A-type stars of peculiarity types other than
CP2/4 hosts a surface-averaged longitudinal magnetic field of more than 3 Gauss. They concluded that there exists
a magnetic dichotomy corresponding to a gap of more than one order of magnitude in field strength.

Furthermore, photometric variability among cool-type (F, G, and K) stars due to the presence of starspots
is a common phenomenon. Nielsen et al. (2013)
published rotational periods of 12 000 main-sequence stars based on observations by the Kepler
satellite mission. As expected, they found that hot stars (earlier than A-type) rotate faster than their
cooler counterparts. However, it is important to connect all these observations to create a global picture
of the rotational behaviour of stars.

In this paper, we present the results of the WASP light curve analysis of bona fide CP2 stars and candidates.
Among the 579 investigated objects, we detected 80 ACVs, from which 74 are reported for the first time.

Observations, target selection, and reductions are described in Sect. 2; data analysis
is characterized in Sect. 3;
results are presented and discussed in Sect. 4. We
conclude in Sect. 5.

2 Observations, target selection and reductions

The main aim of the WASP project is the detection of transiting extrasolar planets.
Two robotic telescopes are employed, which are situated at the Observatorio del Roque de
los Muchachos (La Palma) and the South African Astronomical Observatory (SAAO).
Each telescope consists of an array of eight f/1.8 200mm Canon lenses and
2048 x 2048 Andor CCD detectors, covering a field of 7.8\degrx7.8\degr of sky with an angular size of
13.7\arcsec / pixel (Pollacco et al. 2006). Initially, observations were taken unfiltered;
from 2006 onwards, a broadband filter with a passband from ∼4000 to ∼7000Å was
employed. Each field was observed about every 9 to 12 minutes (Butters et al. 2010).
The first data release (DR1) of the WASP archive, which encompasses light curve data
from 2004 to 2008, boasts ∼18 million light curves covering a large fraction of the sky
and provides good photometry for objects in the magnitude range
8 ≤V≤14 mag.

A list of targets was established by selecting bona-fide CP2 stars from the
Catalogue of Ap, HgMn and Am stars (Renson & Manfroid 2009, RM09 hereafter). The objects
in this catalogue are not explicitly subdivided in the CP groups established by
Preston (1974). We used the listed spectral types therein to distinguish between CP1
stars and the other subgroups (mainly denoted as ‘Si’, ‘Sr’, ‘Sr Eu Si’, ‘He-weak’, ‘Hg Mn’,
and so on). All objects in this list boasting at least 1 000 data points in WASP DR1
were investigated. In total, 579 objects were found to meet these criteria.

The corresponding data were downloaded from the WASP archive at
the computing and storage facilities of the CERIT Scientific Cloud111http://wasp.cerit-sc.cz/(Paunzen et al. 2014).
To avoid the most significant saturation effects, all objects brighter than
V< 8 mag were eliminated.
A lower magnitude cut-off was not deemed necessary as there are only 40 objects in the
RM09 catalogue with V> 14 mag.

3 Data Analysis

As a first step, all light curves were inspected visually and obvious outliers and data points associated to exceedingly
large error bars were removed. The data were then searched for periodic signals in the frequency domain of 0 < f (c/d) < 50
using Period04(Lenz & Breger 2004). Objects exhibiting periodic signals well above the noise level (corresponding to a
semi-amplitude of at least ∼0.005 mag, as determined with Period04) were subjected to a more detailed analysis.
In this second step, the data were binned in order to increase the accuracy of the measurements. Depending on the length
of the dataset, the number and cadence of observations and the quality of the data, different bin-sizes from 0.005 – 0.05 d
were chosen. The data were then carefully cleaned from remaining systematic trends, which were mostly of instrumental
origin or due to blending issues. In addition to that, the data of some stars in the magnitude range 8 <V< 9 mag were
also found to suffer from significant systematic trends likely due to saturation effects (cf. Smalley et al. 2014). In some
cases, the severity of artifacts present in the data necessitated the removal of entire epochs or the complete dataset
of one of the WASP cameras.

WASP observations are often made up of distinctive parts separated by observational gaps of varying length in the data.
Where this applied, shifts in mean magnitude between the corresponding parts of the data were sometimes observed. The
light curves were consequently detrended by shifting all parts of the data to the mean magnitude of the combined dataset.
In some cases, systematic trends introduced spurious periods in the data and might have effectively masked any low-amplitude
variability present. Stars exhibiting a weak signal that could not be attributed to systematic trends but did not produce a
convincing phase plot either, were generally rejected in order to keep the sample free of possibly spurious detections that
might contaminate the sample of derived rotational periods.

The data were searched for periodic signals using the Phase Dispersion Method (PDM) of Stellingwerf (1978) and the Analysis of
Variance (ANOVA) statistic developed by Schwarzenberg-Czerny (1996), as implemented in the PERANSO software package (Paunzen & Vanmunster 2015).
Periods were searched in the range of 0.1 < P (d) < 50. The resulting
power spectra were examined for significant features, and the data were folded with the resulting best-fitting periods and visually inspected.
Objects exhibiting convincing phase plots were considered for inclusion in the final sample. The General Catalogue of Variable Stars (GCVS, Samus et al. 2007 – 2014),
the AAVSO International Variable Star Index, VSX (Watson 2006), the VizieR (Ochsenbein et al. 2000), and SIMBAD (Wenger et al. 2000) databases were
consulted to check for an entry in variability catalogues. Objects that have already been announced as ACV variables in the
literature were dropped from our sample, the only exception being V499 Per, for which only a tentative period has been published in the literature.

It has been shown in the literature that, in most cases, the light curves of CP2 stars can be well represented by a sine wave and
its first harmonic (e.g. North 1984; Mathys & Manfroid 1985; Heck et al. 1987). A least-squares fit to the observations was done using the program
package Period04. Each light curve was fitted using a Fourier series consisting of the fundamental sine wave and its first harmonic,
from which the corresponding amplitudes and their phases were derived. The light curve parameters
(A1, A2, ϕ1, and ϕ2) are listed in Table 1.

The object was finally classified according to spectral type, colour information, period and shape of the light curve. The observed
variability pattern of all stars in the present sample is in accordance with rotational modulation caused by spots.
For some few cases, the discrimination between the light curves of double-waved ACVs and the variability induced by orbital motion
(ellipsoidal variables/eclipsing variables) is not straightforward. As the incidence of ellipsoidal or eclipsing variables among CP2 stars
is very low (Gerbaldi et al. 1985; North & Debernardi 2004; Hubrig et al. 2014; Bernhard et al. 2015), we are inclined to interpret the observed variability as being due to rotational modulation.
The initial period search with Period04 in the frequency range up to 50 c/d also resulted in the discovery of six new δ Scuti
variables. These will be dealt with in an upcoming paper.

Table 1 lists the results and some additional observational data. It is organised as follows:

In agreement with the findings of other investigators, we confirm that WASP data are very well suited to investigate variable stars
with low photometric amplitudes (cf. Smalley et al. 2014).

Figure 1: The light curves of all objects, folded with the period listed in Table 1. The fit curves
corresponding to the light curve parameters given in Table 1 are indicated by the solid lines.Figure 1: continued.Figure 1: continued.Figure 1: continued.Figure 1: continued.

4 Results

The following stars have already been studied in the past and discussed in more detail.

HD 8892:Koen & Eyer (2002) published a period of 1.77945 d based on Hipparcos photometry. Within the
errors, this is in line with our result. Rimoldini et al. (2012) classified it as slowly pulsating B-type star
using automatic classification based on Bayesian networks (probability of 0.58) and the prediction by random forests (probability of 0.33).
The spectral classification of Ap Si (Cowley & Cowley 1965) is consistent with its colours. We are therefore confident that this is a
true CP2 and ACV object.

HD 18410A: The period of 5.08053 d listed by Koen & Eyer (2002) is in agreement with the one derived by us.
Rimoldini et al. (2012) list a variable type of either ‘BE + GCAS’ or ACV depending on the used classification
method.

HD 41251: V448 Aur, there are two different variability types found in the literature. The VSX
catalogue lists it as slowly pulsating B-type star whereas Dubath et al. (2011) list an ACV type. The given
periods are comparable to ours.

HD 131750:Strohmeier et al. (1966) reported variability for this star (NSV 6859). They do not list a period but
a photographic amplitude of 0.35 mag, which - originating in an early type object - is rather large if due
to rotation and/or pulsation. In the same paper, three additional A-type stars of comparable amplitudes are
presented (HD 148891, HD 188297, and HD 204370), which are all eclipsing binary systems. However, our data
show no eclipses, which is also supported by an analysis of Hipparcos data. In addition, the search for roAp
characteristics gave a null result (Freyhammer et al. 2008).

HD 250515: This star is listed in the ASAS Catalogue of Variable Stars (ASAS, Pojmański et al. 2005) as a
’MISC’ type object with a period of 0.47683 d. Wraight et al. (2012) found no variability whereas
Richards et al. (2012) list a period of 0.9116 d and an ACV type (probability of 0.4). The period that produces the best fit to the
WASP data (10.58 d) is much longer than the ones that have been reported before. In order to investigate this issue, we have
combined WASP and ASAS data, with the latter dataset consisting of only 47 datapoints. The 10.58 d period produces the best
fit to the combined data.

HD 279110: This star (V499 Per) is located in the Perseus OB1 association. The period analysis by North (1987)
was not conclusive (possible period of 0.48 or 0.96 d) due to the small number of available observations. From
the WASP data, which have an excellent spatial coverage, we can definitely conclude that 0.94622 d is the correct
period.

In accordance with the findings of previous investigators (e.g. North 1984; Mathys & Manfroid 1985; Heck et al. 1987),
our light curve analysis confirms that the light curves of most CP2 stars can be adequately described by a sine wave
and its first harmonic (cf. Section 3 and Fig. 1.)

For an astrophysical analysis of a possible correlation of the found rotational
periods with age and mass, for example, the location of the individual stars in the
Hertzsprung-Russell-diagram (HRD) has to be estimated. For this, the
effective temperature (or colour) and luminosity (or absolute magnitude) need to be calibrated.
Such calibrations have been especially developed and tested for the different CP subgroups (Maitzen et al. 1980; Netopil et al. 2008)
but they all require some additional information such as photometric data in various systems,
an estimation of the reddening, and, most important, knowledge of the distance.

For all stars, Johnson BV(Kharchenko 2001) and 2MASS (Skrutskie et al. 2006) colours are available. The errors
for (B−V) are between 0.01 and 0.2 mag whereas they are between 0.02 and 0.05 mag for (J−H).
For only four stars (HD 30335, HD 109030, HD 1237040, and HIP 109911), the complete Strömgren uvbyβ
measurements are available.

With these sparse data, it is not possible to calibrate the reddening of our sample stars.
We therefore used the Galactic location of our targets to calculate the maximum reddening using the
model by Schlafly & Finkbeiner (2011), who obtained reddening as the difference between the measured and predicted
colours of a star as derived from stellar parameters from the Sloan Digital Sky Survey.
For our sample, we find a maximum of E(B−V) = 1.92 mag, with a mean of 0.43 mag and a median of
0.33 mag, respectively. Bearing in mind that the total absorption AV = 3.1E(B−V), the
importance of a reasonable determination is obvious. For none of our targets, a parallax measurement
with an accuracy better than 20% is available (van Leeuwen 2007). Taking into account the above listed limitations,
we are not able to give reliable astrophysical parameters for the investigated objects.

5 Conclusion

We have carried out a search for photometric variability in confirmed or suspected CP2 stars from the Catalogue of
Ap, HgMn, and Am stars (RM09) using the publicly available observations from WASP DR1. Around 3 850 000 individual
photometric measurements were analysed, which resulted in the discovery of 80 variables, from which 74 are reported
here for the first time. Among this number are 23 stars which had been reported as probably constant in the literature
before. In agreement with the literature, our light curve analysis confirms that the light curves of most CP2 stars
can be adequately described by a sine wave and its first harmonic.
Because of the scarcity of suitable photometric data and the lack of parallax measurements with an accuracy
better than 20%, we are not able to give reliable astrophysical parameters for the investigated objects.

Acknowledgements.

The WASP project is funded and maintained
by Queen’s University Belfast, the Universities of Keele, St.
Andrews, Warwick and Leicester, the Open University, the Isaac
Newton Group, the Instituto de Astrofisica Canarias, the South
African Astronomical Observatory and by the STFC. This project was supported by the SoMoPro II Programme (3SGA5916),
co-financed by the European Union and the South Moravian Region, the
grant GA ČR 7AMB12AT003, LH14300, and
the financial contributions of the Austrian Agency for International
Cooperation in Education and Research (BG-03/2013 and CZ-09/2014).
This work reflects the opinion of the authors and the European
Union is not responsible for any possible application of the information
included in the paper.